What is the asymptotes of 3x^2-y^2+6x-2y=10 ?

The asymptotes of 3x^2-y^2+6x-2y=10 is y=sqrt(3)(x+1)-1,\quad y=-sqrt(3)(x+1)-1

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asymptotes of 3x^2-y^2+6x-2y=10

asymptotes

3 x^{2} - y^{2} + 6 x - 2 y = 10

y = 3 (x + 1) - 1, y = - 3 (x + 1) - 1

Solution steps

y = \pm \frac{b}{a} (x - h) + k

Calculate Hyperbola properties

3 x^{2} - y^{2} + 6 x - 2 y = 10 :

Right-left Hyperbola with

(h, k) = (- 1, - 1), a = 2, b = 23

y = \frac{2 3}{2} (x - (- 1)) + (- 1), y = - \frac{2 3}{2} (x - (- 1)) + (- 1)

Refine

y = 3 (x + 1) - 1, y = - 3 (x + 1) - 1

\frac{( x - 1 ) ^{2}}{9} - \frac{( y + 6 ) ^{2}}{4} = 1

\frac{x ^{2}}{16} - \frac{y ^{2}}{20} = 1

y^{2} - 4 x^{2} = 16

\frac{x ^{2}}{36} - \frac{y ^{2}}{25} = 1

\frac{( x - 3 ) ^{2}}{3} - \frac{( y - 2 ) ^{2}}{2} = 1

What is the asymptotes of 3x^2-y^2+6x-2y=10 ?
The asymptotes of 3x^2-y^2+6x-2y=10 is y=sqrt(3)(x+1)-1,\quad y=-sqrt(3)(x+1)-1